Title: The Picard Group of the Stable Module Category for Quaternion Groups
Speaker: Richard Wong
Speaker Info: UT Austin
One problem of interest in modular representation theory of finite groups is in computing the group of endo-trivial modules. In homotopy theory, this group is known as the Picard group of the stable module category.Date: Tuesday, October 13, 2020
This group was originally computed by Carlson-Thévenaz using the theory of support varieties. However, I provide new, homotopical proofs of their results for the quaternion group of order 8, and for generalized quaternion groups, using the descent ideas and techniques of Mathew and Mathew-Stojanoska. Notably, these computations provide conceptual insight into the classical work of Carlson-Thévenaz.